Bay Area (Census Tract-level) maps of PM 2.5 (red) and Asthma (green).

Before analyzing the maps above, I want to clarfiy what the CalEnviroScreen data respresents and conveys. As for PM 2.5, this measure communicates the levels of particulate matter – one of the six US EPA criteria air pollutants – in the atmosphere. PM 2.5 can move deep into the lungs, cause lung disease, and contribute to death. CalEnviroScreen specifically relies on air monitoring stations across the state to collect data. As for the 4.0 version of the model, it uses the annuaal mean concentration of PM 2.5 (averaging monitor and satellites measurements) over the three-year period fo 2015-17. PM 2.5 is reported in µg/m3. Transitioning to Asthma, this variable refers to the chronic lung disease in which those suffering experience episodes of breathlessness, tightness in the chest, and coughing/wheezing. Research shows that exposure to traffic and air pollutants contribute to asthma attacks. Sensitive populations include children, the elderly, and low-income individuals. CalEnvroScreen reports asthma as the “spatially modeled, age-adjusted rate of ED (emergency deparment) visits for asthma per 10,000.” In the 4.0 model, it is averaged over the three-year period of 2015-17.

Looking at the maps, one can see that the highest PM 2.5 measures come from the East Bay, particularly in the Oakland, Richmond, and Vallejo areas. Additionally, it appears that Napa represents a PM 2.5 hotspot. As for Asthma, the highest rates of prevalence appear in Vallejo, Richmond, Antioch, and just North of San Leandro. I see correlation between the two maps. However, PM 2.5 levels seem high throughout most of the East Bay (with values over 8 µg/m3), whereas asthma is more concentrated into specific regions. This may indicate that another variable (on top of PM 2.5) helps to control the prevelance of asthma in the Bay Area.

Scatterplot of PM 2.5 and Asthma for Bay Area (with linear best fit line).

## 
## Call:
## lm(formula = Asthma ~ PM2.5, data = .)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -54.47 -25.89  -9.61  12.94 182.95 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -116.278     13.040  -8.917   <2e-16 ***
## PM2.5         19.862      1.534  12.950   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 37.49 on 1578 degrees of freedom
## Multiple R-squared:  0.09606,    Adjusted R-squared:  0.09549 
## F-statistic: 167.7 on 1 and 1578 DF,  p-value: < 2.2e-16

The original best fit line for the scatterplot (blue) does not appear to fit the dataset particularly well, given the fac that the distribution does not mirror that of a linear relationship. For instance, the vertical rise of points between 8-9 µg/m3 of PM 2.5 represents a pivot from the previous trend of a slopeless linear line. Looking at the summary of the linear regression analysis, the residuals are neither centered around 0 nor are they symmetric in their distribution. The standard error is 1.534 on a slope of 19.862, and the r-squared value is .096. In layman’s terms, an increase of 1 µg/m3 in PM 2.5 is associated with an increase of 19.862 ED visits for asthma per 10,000 in asthma occurence; 9.6% of the variation in asthma is explained by the variation in PM 2.5.

Density profile of linear rergression’s residuals.

## NULL

The density profile of the linear regression’s residuals appears significantly skewed to the right, suggesting that a straight best fit line may not be the best approach. Additionally, unlike a normal distribution of residuals, this one is also not centered at 0.

Scatterplot of PM 2.5 and log(Asthma) for Bay Area (with linear best fit line).

## 
## Call:
## lm(formula = log(Asthma) ~ PM2.5, data = .)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.00402 -0.46479  0.03313  0.42298  1.75525 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.69234    0.22840   3.031  0.00248 ** 
## PM2.5        0.35633    0.02686  13.264  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6566 on 1578 degrees of freedom
## Multiple R-squared:  0.1003, Adjusted R-squared:  0.09974 
## F-statistic: 175.9 on 1 and 1578 DF,  p-value: < 2.2e-16

Density profile of linear rergression’s residuals with log transformation of data.

## NULL

Under a log transformation, the residuals are centered around zero and more symmetrical. Further, the standard error is .02686 on a slope of .35633, while the r-squared value comes in a .1003. In layman’s terms, an increase of 1 µg/m3 in PM 2.5 is associated with an increase of .35633 log(ED visits for asthma per 10,000) – which corresponds to a 44% increasse in ED visits for asthma per 10,000; 10.03% of the variation in log(asthma) is explained by the variation in PM 2.5. Once again the data does not seem to fit the geom_smooth best fit line particularly well. The histogram density distribution of residuals looks much more promising. I do notice the dip at zero, but overall this is more normal than without the transformation.

Map of residuals (Census-Tract level) in Bay Area.

##             1             2             3             4             5 
##  1.3616534971  0.8011945744  1.3609604315  1.4296462016  1.0092724408 
##             6             7             8             9            10 
##  1.7011920718  1.3636190758  0.7538386530  1.1571072816  1.1503125941 
##            11            12            13            14            15 
##  0.8717112614  1.1475073867  0.9973043315  1.3027113339  1.1093311211 
##            16            17            18            19            20 
##  0.9930094581  1.1497604946  1.5471204239  0.6311594651  0.7068761059 
##            21            22            23            24            25 
##  1.2845893825  1.5114990104  0.7914324841  0.8629900388  0.7299148950 
##            26            27            28            29            30 
##  1.0032043511  1.5393760320  0.3876135277  0.9526847862  0.5967626691 
##            31            32            33            34            35 
##  0.7631842044  1.0378771406  1.0706237323  1.0804355385  0.5542398182 
##            36            37            38            39            40 
##  0.4403673092  1.1233551820  1.2564454561  0.9231475691  1.0825044727 
##            41            42            43            44            45 
##  0.2885350179  0.6618652703  0.2586929157  0.3527158785  0.7396429125 
##            46            47            48            49            50 
##  0.9930094581  1.0032043511  0.9658254631  0.8719035795  1.0802270313 
##            51            52            53            54            55 
##  1.1061065899  0.2643239504  0.8280919847  0.7968302614  0.9744103644 
##            56            57            58            59            60 
##  0.8234579692  0.9112622001  0.9890503328  0.8644350512  0.1067772965 
##            61            62            63            64            65 
##  1.0106610762  0.4183334672  0.6665677556  0.5216626395  0.4070071469 
##            66            67            68            69            70 
##  0.5243072586  0.6111846846  0.7168387920 -0.2391340386  0.7124779806 
##            71            72            73            74            75 
##  1.3578603233  1.0726464468  0.0708961999  1.0528042069  1.0953919736 
##            76            77            78            79            80 
##  1.6023009574  0.1369176824  1.1506928588  0.6586786637  0.8719773141 
##            81            82            83            84            85 
##  1.2921762330  1.3608761637  1.3146022471  0.7792582372  1.6333702176 
##            86            87            88            89            90 
##  0.5827524992  1.1620333987  0.0182110472  0.1219271496  1.1208096299 
##            91            92            93            94            95 
##  0.3478299750  1.3659875038  0.7486820022  0.5281743260  0.5081556203 
##            96            97            98            99           100 
##  0.5361517016  1.3380022545  0.2967890259  0.7192322641  0.4143976912 
##           101           102           103           104           105 
##  0.7773163197  0.6131132786  0.4629801800  0.7332257573  0.7008559119 
##           106           107           108           109           110 
##  0.9944472984  0.3779196631  1.0255088515  1.2686054382  1.1084766426 
##           111           112           113           114           115 
##  0.6742548093  1.3823667466  0.9681493727  0.4329645254  0.2896174473 
##           116           117           118           119           120 
##  0.7168289730  1.1739389815  0.0429667042  0.3479017596  0.4822892772 
##           121           122           123           124           125 
##  0.5114167104  0.3439304064  0.7411546655  1.0805917421  0.5824914327 
##           126           127           128           129           130 
##  0.6409341709  0.5113451868  1.1195106099  1.1272071030  1.3105725062 
##           131           132           133           134           135 
##  0.3658065801  1.3985202875  0.7924195235  0.9867712311  1.5463561705 
##           136           137           138           139           140 
##  0.5879747405  0.5099769525  1.3899637155  0.7607655030  1.2561741259 
##           141           142           143           144           145 
##  0.0843656861  0.2407494857  0.9903269887  0.2125813985  0.1507104819 
##           146           147           148           149           150 
##  1.0187692681  1.0038971490  0.3861727923  0.7068761059 -0.2400157327 
##           151           152           153           154           155 
##  0.6970072421  0.5532309287  0.4006391925  1.1494949534  0.6728836522 
##           156           157           158           159           160 
##  0.8174297614  0.6011187777  0.7481288525  0.5088824087  1.7552517606 
##           161           162           163           164           165 
## -0.2879069923  0.4983460875  0.4580493880  0.5827524992  0.5906487073 
##           166           167           168           169           170 
##  0.3752774308  0.6175529023  1.4083246604  0.2722622091  0.8214262628 
##           171           172           173           174           175 
##  0.1143272277 -0.1048203384 -0.0884144201  0.8318957968  0.3564973375 
##           176           177           178           179           180 
##  0.2663531966 -0.5153613664  0.8466637487  0.2604303801  0.7501376187 
##           181           182           183           184           185 
##  0.4886072663  0.0456050164 -0.6934687884  0.6833334275  1.3535367740 
##           186           187           188           189           190 
##  0.2145417690 -0.0364079503  1.2801871107  0.8784795626  1.1502188477 
##           191           192           193           194           195 
##  0.0598492171  1.1396846309  0.8892579524  0.6001323294  0.9040157329 
##           196           197           198           199           200 
##  0.3378932946  0.3110417066  0.1972359360  0.0427735856  0.7571525232 
##           201           202           203           204           205 
##  0.1794406265 -0.0588448178  0.7675373190 -0.4169187345  0.2625890233 
##           206           207           208           209           210 
##  0.2467267510  0.4173181927  0.5837920650  0.1125689220  1.3948606105 
##           211           212           213           214           215 
##  0.5892765084  0.4097543582  0.4015750835  0.2815047569  0.6264313271 
##           216           217           218           219           220 
##  0.1364787951  0.4173231693  0.7055375511  0.4115661583  0.3006885636 
##           221           222           223           224           225 
##  0.7517545747  1.2388298437  0.4351615827  0.4692108851  0.4846473056 
##           226           227           228           229           230 
##  0.5450822823  0.7787288085  0.8050723067  0.7748054745  0.4802837822 
##           231           232           233           234           235 
##  1.1914946972  0.4216762266  1.3283049591  0.6526672888  0.3609560324 
##           236           237           238           239           240 
##  0.2145291652  0.5242033800  1.4842675455  0.2631839240  0.9231934732 
##           241           242           243           244           245 
##  0.7369013255  1.5071834744  0.3377771065  0.3100133933  0.3778356659 
##           246           247           248           249           250 
##  0.3944603594  0.1506413135  0.8135593845  0.5445148880  0.5379779090 
##           251           252           253           254           255 
##  0.1840541389  0.0922817582  1.0500186696  0.8288576571  0.4818411562 
##           256           257           258           259           260 
##  0.0883512565  0.7786883191  0.7192322641  1.4509719274  0.3419427036 
##           261           262           263           264           265 
##  0.9420425955  1.4128399689  0.4933992976  0.8450249846  0.8592886069 
##           266           267           268           269           270 
##  0.0730232491  0.7218206793  0.7361557659 -0.2326068159  0.3954853931 
##           271           272           273           274           275 
##  0.5627585118 -0.2337074710  0.6420402355  0.3639661417  1.3394771347 
##           276           277           278           279           280 
##  1.2184660893 -0.0937509749  0.2480847133  0.6661243405  1.1379762858 
##           281           282           283           284           285 
## -0.2549270219  1.5007529286  0.7348181925  0.5315022043  0.3671205802 
##           286           287           288           289           290 
##  0.4527795242  0.3766281718  0.9132143371  0.2797741841  0.2313827396 
##           291           292           293           294           295 
##  0.3311865267 -0.0255064980  0.2424423742  0.4097543582  0.8814815417 
##           296           297           298           299           300 
## -0.0697581504  0.6807798224  0.3309156165  0.3607178572  0.8540305286 
##           301           302           303           304           305 
##  0.0795608137 -0.1121752508 -0.3819577589  0.1335718238  0.4993596180 
##           306           307           308           309           310 
##  0.4669212211  0.2575570358  0.3286379049 -0.2847301752  0.3083782543 
##           311           312           313           314           315 
##  0.2028997412  0.5873085299  0.4575236420 -0.4485870283  0.1927140474 
##           316           317           318           319           320 
## -0.1022682547  0.6292248201  0.8774390922 -0.2583512165  0.7266849642 
##           321           322           323           324           325 
##  0.4555145080 -0.3364462543  0.4773157475  0.9699209809  0.4809592540 
##           326           327           328           329           330 
##  0.9401527142  0.4530140992  0.4224955480  0.2106619168  1.1553070516 
##           331           332           333           334           335 
##  0.3247615436  0.7500290089  1.7473922775  0.6661118078  0.9713487824 
##           336           337           338           339           340 
##  0.3218627349  0.8943988776  0.1794406265  0.6613684322 -0.1423344076 
##           341           342           343           344           345 
##  0.8577179587  0.2037971231  1.2247839254  0.4172128887  0.5566592520 
##           346           347           348           349           350 
##  0.4983460875  0.2991220388  0.1892318087  0.8505087835  0.4762773840 
##           351           352           353           354           355 
##  0.1606293484  1.5125944796 -0.4035510687  0.2360380854  0.0331113634 
##           356           357           358           359           360 
## -0.4285820996  0.3256886526  0.3909674933  0.2897524200 -0.1837608100 
##           361           362           363           364           365 
## -0.8135649315 -0.2354362509  1.0947558311  0.4068435595  0.8523622475 
##           366           367           368           369           370 
##  0.2667861731  0.5637046396  0.3130437048  1.4488603922  0.4172128887 
##           371           372           373           374           375 
##  1.0778645930  0.0282947640  0.6617157374  0.5868253616  0.8449555556 
##           376           377           378           379           380 
##  0.2100164865  0.3658814192 -0.1694844118  0.0525490457  0.3427151831 
##           381           382           383           384           385 
##  0.1993659246  0.3180989456 -0.5982710125  0.1065488987  1.3943839645 
##           386           387           388           389           390 
##  1.2210888400  0.0758253404  0.1764066624  0.4427113573 -0.0969373687 
##           391           392           393           394           395 
##  0.3514421907 -0.8721764675 -0.5249471225  0.7192322641  0.8454190836 
##           396           397           398           399           400 
## -0.2982000203  1.0175800012  0.3995627544 -0.2014549625  0.6995308265 
##           401           402           403           404           405 
##  0.7324689730  0.1152151162  0.1925446629  1.2810468389  0.1696868335 
##           406           407           408           409           410 
##  0.5864327944  0.4560142065  0.2081980281  0.4714026846  0.2719648024 
##           411           412           413           414           415 
##  0.3225609505 -0.0342150650  0.6890339926  1.0688412640  0.5687169013 
##           416           417           418           419           420 
## -0.1327074716  0.2971081317  0.8572193087  0.5811578035  0.1627710241 
##           421           422           423           424           425 
## -0.3934139186 -0.2873402002 -0.6672165750  0.1582829308  0.4158316387 
##           426           427           428           429           430 
##  0.2484555338 -0.2973608549 -0.0025294677  0.0121295720  0.3093244223 
##           431           432           433           434           435 
##  0.8814815417  1.3207512801  1.3640033399  0.1123024593  0.5188628299 
##           436           437           438           439           440 
##  0.9631484443  0.1088530859  0.1973230868 -0.1683172644  0.4380046094 
##           441           442           443           444           445 
##  0.1794494044  1.2977869355  1.0113101933  0.1015377060 -0.5043917133 
##           446           447           448           449           450 
##  0.7334378635  0.6466115531 -0.3397863509  0.1311205267  1.1512314332 
##           451           452           453           454           455 
## -0.0697581504  0.4613133687 -0.2252575863  0.5132786503  0.3959189898 
##           456           457           458           459           460 
##  0.3155605672  0.2488063471  0.3278717646  0.0315703963 -0.4839531659 
##           461           462           463           464           465 
##  0.3344775287  0.4192910831  0.0440609830  0.8636885945 -0.3454331881 
##           466           467           468           469           470 
## -0.6660313560  0.1127470217 -0.2505489970  0.0516776356  0.3249446440 
##           471           472           473           474           475 
## -0.4778494213  0.2109551075  0.2346021840  1.1623258411 -0.1327735322 
##           476           477           478           479           480 
##  0.6761803966 -0.5332698889  0.6090559840 -0.3700193086 -0.3187418808 
##           481           482           483           484           485 
## -0.6796084009  0.1348554870  0.8540305286  1.4253318987 -0.3774347692 
##           486           487           488           489           490 
## -0.0234772891  0.1913977652  0.1983940476  0.3203988160 -0.2890301822 
##           491           492           493           494           495 
##  0.5030671682  1.4110234283  0.1437227494 -0.3296172441  0.7534477097 
##           496           497           498           499           500 
## -0.8461725890 -0.2675795757 -0.4287323291  0.4172128887  0.1663572905 
##           501           502           503           504           505 
##  0.2319098384 -0.0697581504 -0.0213568947  0.3312735185  0.6248977351 
##           506           507           508           509           510 
## -0.0518935541 -0.2786248917  0.5006596309  0.5990795064  0.7142715006 
##           511           512           513           514           515 
##  0.3188430016 -0.6682375352 -0.5228575334  0.3594507355 -0.4278763494 
##           516           517           518           519           520 
##  0.3436240403  0.4310895362  0.3502336657  1.4083246604  0.2686940060 
##           521           522           523           524           525 
## -0.7200749711  0.5412931667  0.1333958769  0.6099029757  0.2433946124 
##           526           527           528           529           530 
##  0.4514546741 -0.1649913708  0.3760917783 -0.2813490571  0.4928202505 
##           531           532           533           534           535 
##  0.9915010159  0.1983267449  0.2118701262 -1.0832474610 -0.2070576367 
##           536           537           538           539           540 
##  0.1264827693 -0.3105532108  0.0208439744 -0.6720182775  1.2126124179 
##           541           542           543           544           545 
## -0.6194179306 -0.0276404129 -0.3576920680  0.4272858633 -0.5405683377 
##           546           547           548           549           550 
##  0.5973898254 -0.8136340055  0.3784931815  0.2453723317 -0.1619643905 
##           551           552           553           554           555 
## -0.3462117281  0.4056936403  0.3311865267  0.5826798190 -0.1121752508 
##           556           557           558           559           560 
## -0.0679041287 -0.5120647949 -0.4246247642  0.1975221160  0.9622888589 
##           561           562           563           564           565 
## -0.3023407568  0.8537287868  0.2088189968  0.0937391722 -0.3562463238 
##           566           567           568           569           570 
##  0.6458899409  0.0899275687  0.4107682326 -0.2064230350  0.0239057664 
##           571           572           573           574           575 
##  0.1697723060  0.1680907819  0.6330065853  0.2006607413 -0.2629158037 
##           576           577           578           579           580 
##  0.8942641537  0.9421230869  0.2146825816  0.1176412104  0.7065601616 
##           581           582           583           584           585 
##  0.3394887033 -0.3737976897 -0.1440169635  0.3047838427  0.4172128887 
##           586           587           588           589           590 
## -0.6593312724  0.3051540489  0.3277782683  0.1628316736  0.1582829308 
##           591           592           593           594           595 
##  0.0355252932  0.3431164455 -0.2498882202  0.0004553732 -0.2760273949 
##           596           597           598           599           600 
## -0.6139108892  0.5480437177  0.8112043915  0.1143272277 -0.3189422187 
##           601           602           603           604           605 
##  0.3539051672  0.2014301305 -0.3813821571 -0.0079858431 -0.0961845716 
##           606           607           608           609           610 
##  0.2172365692 -0.3177454769 -0.2290521293  0.9541369365  0.0447715287 
##           611           612           613           614           615 
##  0.4045808543 -0.3636697972  0.3654435879 -0.3001681978  0.4655861625 
##           616           617           618           619           620 
##  0.4315351407  0.3157480766  0.4905985006  0.0690092930  0.2126676568 
##           621           622           623           624           625 
##  0.4483106281  0.0631570534 -0.3557028257  0.5892905248 -1.0996870685 
##           626           627           628           629           630 
## -0.2817904765 -0.4819204926 -0.2090089355  0.1463189709 -0.2354667773 
##           631           632           633           634           635 
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##           996           997           998           999          1000 
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##          1001          1002          1003          1004          1005 
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## -0.1256916633 -0.6861335253  0.0496079584 -1.4840130204 -0.8512926118 
##          1011          1012          1013          1014          1015 
## -0.2486568418 -0.3570063351 -0.4470057803 -0.0826030148 -0.4727285842 
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## -0.1268713702 -0.3741183945 -0.2941134057  0.2771473727 -0.4950406503 
##          1021          1022          1023          1024          1025 
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##          1026          1027          1028          1029          1030 
## -0.2188525942 -0.0194613953 -0.4627697548  0.0331419534 -0.1964485392 
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## -0.6107614328 -1.2797887699 -1.0109619929  0.3450034218 -1.3201297083 
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## -0.4642615034 -0.5178230916  0.0162315912 -0.8391798800 -0.2294738325 
##          1041          1042          1043          1044          1045 
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##          1056          1057          1058          1059          1060 
##  0.5964909228 -0.4241466051 -0.2730916286 -0.1646924898 -0.8553033533 
##          1061          1062          1063          1064          1065 
##  0.1353021586 -1.0443785164 -0.2640015036  0.6896994899 -0.2399345434 
##          1066          1067          1068          1069          1070 
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##          1071          1072          1073          1074          1075 
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##          1076          1077          1078          1079          1080 
## -0.5249584177 -1.0028548325 -0.6894877708 -0.6276196235 -0.9516324126 
##          1081          1082          1083          1084          1085 
## -0.4162181402 -0.6255888378 -0.8672775806 -0.5956201480 -0.8007397346 
##          1086          1087          1088          1089          1090 
## -0.8536594892  0.3817164254 -0.2803603008  0.3469743207 -0.4778651806 
##          1091          1092          1093          1094          1095 
## -0.2574832945 -0.6280650832 -0.2793460952 -0.4233608423  0.8673940967 
##          1096          1097          1098          1099          1100 
##  0.1731856467 -0.3742391437 -0.3372031902 -0.6313084835  0.0274389854 
##          1101          1102          1103          1104          1105 
## -0.3699814191  0.0108175572 -0.2801126550  0.2768003351 -0.6683259167 
##          1106          1107          1108          1109          1110 
## -0.6081009600 -0.6081567310 -0.9302643755 -0.2275125399 -1.4572241138 
##          1111          1112          1113          1114          1115 
##  1.1258949325 -0.9009798845 -0.7551070311 -0.4237982702 -0.3918803188 
##          1116          1117          1118          1119          1120 
## -0.0323037166 -0.5919070677 -0.2207081440  0.6614216522 -0.6591047910 
##          1121          1122          1123          1124          1125 
## -0.8386120904 -0.3362789951 -0.7931826954 -0.7401833472 -0.9961880953 
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## -1.0583716162  0.3181214746  0.3590281785 -0.6785083033 -0.2001399798 
##          1131          1132          1133          1134          1135 
## -1.2319284512 -0.5695331062 -0.5460054889  0.2359132678 -0.7565048706 
##          1136          1137          1138          1139          1140 
## -0.5300455287 -0.3310663364 -1.1149087302  0.2256488436  0.3882563543 
##          1141          1142          1143          1144          1145 
## -0.1352351917 -0.2699204266 -0.8248715090  0.1042535215 -1.2363867471 
##          1146          1147          1148          1149          1150 
## -0.5221835713 -0.7193470344 -0.2249953306 -1.1184974063 -0.1993049585 
##          1151          1152          1153          1154          1155 
## -0.3769808510  0.3335607255 -0.9848627038  0.2481602902  0.2311669846 
##          1156          1157          1158          1159          1160 
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##          1161          1162          1163          1164          1165 
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##          1166          1167          1168          1169          1170 
## -0.7011838106 -0.1925029800 -0.4270946316 -0.3368918176  0.1999335781 
##          1171          1172          1173          1174          1175 
## -0.2711234181 -0.5683840574 -0.2392305336 -0.9078507586 -0.2273294895 
##          1176          1177          1178          1179          1180 
## -1.0210787895  0.4627983318 -0.4324058506  0.3636738814 -0.4246680829 
##          1181          1182          1183          1184          1185 
## -0.2335326149 -0.1988607093 -0.5621664900 -0.0467012047 -0.1896261050 
##          1186          1187          1188          1189          1190 
##  0.0380705861 -0.5044546844 -0.5834788201 -1.2139599818 -0.2814180486 
##          1191          1192          1193          1194          1195 
## -0.4970748749  0.1296004656 -0.3956805841  0.0942657562 -0.8007397346 
##          1196          1197          1198          1199          1200 
## -0.1520908914 -1.1618764874 -0.3988824405  0.2365564965  0.3452086758 
##          1201          1202          1203          1204          1205 
## -0.2589106600 -0.3761863276 -1.2766973806 -0.3500242988 -0.1149495518 
##          1206          1207          1208          1209          1210 
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##          1211          1212          1213          1214          1215 
## -0.3465920640 -0.8298610121 -0.0658862175  0.0429861833  0.2801960440 
##          1216          1217          1218          1219          1220 
## -0.9901486120 -0.8463214328 -0.2187391645  0.0425314947  1.2562359190 
##          1221          1222          1223          1224          1225 
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##          1226          1227          1228          1229          1230 
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##          1231          1232          1233          1234          1235 
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##          1241          1242          1243          1244          1245 
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##          1246          1247          1248          1249          1250 
## -0.1847877381 -0.5713587214 -0.2958863156 -0.8007397346  0.0422397486 
##          1251          1252          1253          1254          1255 
## -0.6632928390 -0.4925242990  0.0425447000  0.6101420436 -0.3395678543 
##          1256          1257          1258          1259          1260 
## -1.0332275581 -0.5365607365 -0.4079245960  0.0321459453  0.9416541192 
##          1261          1262          1263          1264          1265 
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##          1266          1267          1268          1269          1270 
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##          1271          1272          1273          1274          1275 
## -0.6120929386  0.3437693665  0.6898150961 -0.0244600928 -0.6047397607 
##          1276          1277          1278          1279          1280 
## -0.2259142089 -0.2696305619 -0.2305210202  0.3712998815 -0.7673070867 
##          1281          1282          1283          1284          1285 
## -0.2414027021 -0.6924420835 -0.6752150366 -1.1598885870 -0.1528491941 
##          1286          1287          1288          1289          1290 
## -0.2764849617  0.2316365452  0.1131701097 -0.1654770368 -0.6487600382 
##          1291          1292          1293          1294          1295 
##  0.2082463355  0.1086114484  0.0771851397  0.3985970698 -0.4507651462 
##          1296          1297          1298          1299          1300 
## -1.4756273817 -0.6013525652 -0.5941379511 -0.4466395175 -0.2556119954 
##          1301          1302          1303          1304          1305 
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##          1306          1307          1308          1309          1310 
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##          1311          1312          1313          1314          1315 
## -0.0731890748  0.0697420908 -0.4553597825 -0.4836458463 -0.4433494922 
##          1316          1317          1318          1319          1320 
## -1.0735978529 -1.3467006961 -0.0438574081  0.1196255696 -0.8407205894 
##          1321          1322          1323          1324          1325 
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##          1326          1327          1328          1329          1330 
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##          1331          1332          1333          1334          1335 
## -0.6159050921  0.2835457051 -0.1418466342 -0.4818203549 -0.2324372171 
##          1336          1337          1338          1339          1340 
## -1.3229287784 -1.1676516468  0.0395367528 -0.1446515438 -0.3687844990 
##          1341          1342          1343          1344          1345 
## -1.0602370162 -0.4251370170 -0.8651419590  0.0602102035 -1.3209722856 
##          1346          1347          1348          1349          1350 
## -0.6692413300 -0.7629788950 -0.1685156728 -0.5104259296 -0.4196775193 
##          1351          1352          1353          1354          1355 
## -0.2538921901 -0.8611660608  0.3541536038 -0.6507782204 -1.0302948831 
##          1356          1357          1358          1359          1360 
## -0.1014433616 -0.7546819997  0.1208572854 -0.2049756490 -0.0487779488 
##          1361          1362          1363          1364          1365 
## -0.7432345040 -0.4159195242 -0.3844616585 -0.3040873466 -0.2016166838 
##          1366          1367          1368          1369          1370 
## -0.4879715118 -0.7869113023  0.2870058226  0.2989715988 -0.8055010050 
##          1371          1372          1373          1374          1375 
## -0.7837913958 -0.3059363865 -0.3924214843 -1.0484662483 -0.8518369951 
##          1376          1377          1378          1379          1380 
## -0.5028940736 -0.2033296104  0.2689232723 -0.5894729202 -0.4663789074 
##          1381          1382          1383          1384          1385 
## -1.5329788362 -0.2995617133 -0.5316879361 -0.6035458841 -0.5575423404 
##          1386          1387          1388          1389          1390 
## -0.5423559546 -0.1974993287 -0.1776979849 -0.8817471082 -0.4286879868 
##          1391          1392          1393          1394          1395 
## -0.4326939478 -0.1142697838 -0.0730630354  0.4665141812  0.1644551023 
##          1396          1397          1398          1399          1400 
## -1.2434921658 -0.8042809697 -1.2051908400 -1.0892109219 -0.4821570023 
##          1401          1402          1403          1404          1405 
## -0.3052910577 -0.5807108108 -0.6317471515 -0.7426228146 -0.9368899433 
##          1406          1407          1408          1409          1410 
## -0.5962693430 -1.0317458774  0.2908798556 -0.5060257673 -0.3949364367 
##          1411          1412          1413          1414          1415 
## -1.1318987101 -0.0370572538  0.3634997662 -0.8782268857 -0.5038370557 
##          1416          1417          1418          1419          1420 
## -1.2004060594 -0.8250061734 -0.6957765600 -1.0883107880 -0.0394579208 
##          1421          1422          1423          1424          1425 
## -0.7569465716 -1.3532110553 -1.0706505825 -0.5567093039 -0.4433790313 
##          1426          1427          1428          1429          1430 
## -1.1358075712 -1.3247038204 -0.2993985267 -0.6176407584 -0.5668599301 
##          1431          1432          1433          1434          1435 
## -0.4890534854 -0.2935077366 -0.4264522237 -0.5356883184 -1.0061840553 
##          1436          1437          1438          1439          1440 
##  0.2250431481 -0.7446528170  0.6468336021 -0.6463525787 -0.5763678802 
##          1441          1442          1443          1444          1445 
## -0.9868500153 -0.8024894446 -0.4859533776 -1.1322047392 -1.4858138623 
##          1446          1447          1448          1449          1450 
## -0.6752708726 -0.8920071661 -0.0122429239 -0.4138027184 -0.2352839687 
##          1451          1452          1453          1454          1455 
##  0.3372834078 -0.7677666554 -0.1976512188 -1.0624199513 -0.9101385966 
##          1456          1457          1458          1459          1460 
## -1.2977500638 -0.4739863100 -0.5926159884 -0.6312516461 -1.3615151834 
##          1461          1462          1463          1464          1465 
## -0.1925725797 -0.3467563782 -1.3624400111 -0.9912724021 -0.3015111468 
##          1466          1467          1468          1469          1470 
## -0.4787883077 -0.6157120231 -0.5253313655 -0.7254565507 -1.2390756736 
##          1471          1472          1473          1474          1475 
## -0.9222963705 -0.8283717623 -0.6133562181 -1.1336040990 -0.3536387046 
##          1476          1477          1478          1479          1480 
## -0.7208605368  0.1548000782 -1.0169412153 -1.0033586748 -0.9878172094 
##          1481          1482          1483          1484          1485 
## -0.2884384944  0.1249239073 -1.5177465197 -0.4284720959 -0.6381058618 
##          1486          1487          1488          1489          1490 
## -0.7148761081  0.3096043900 -0.5589802750 -1.5038481885 -1.0102250905 
##          1491          1492          1493          1494          1495 
## -0.8253976777 -1.3695810320 -0.6192065378 -0.7404155016 -1.0141890160 
##          1496          1497          1498          1499          1500 
## -0.4737609223 -1.3654970098 -1.0146829012 -0.4035057687 -1.3511452302 
##          1501          1502          1503          1504          1505 
## -0.8842527637 -1.0760410024 -1.0740496548 -1.3449292895 -1.3762830967 
##          1506          1507          1508          1509          1510 
## -0.7638514889 -1.0627487937 -0.6488210085 -0.7197248075 -0.5649716356 
##          1511          1512          1513          1514          1515 
## -0.7201313883 -0.7626695592 -0.2151854655 -1.0809703679 -0.7936604271 
##          1516          1517          1518          1519          1520 
## -0.3574624151 -0.9170600525 -1.1596153341 -0.4957285770 -0.4776401200 
##          1521          1522          1523          1524          1525 
## -0.8006577930 -1.0138035262 -1.0990921201 -0.9720099642 -0.5441936078 
##          1526          1527          1528          1529          1530 
## -1.0304439861 -0.1367351717 -0.6471456417 -1.3697163460 -0.7465791245 
##          1531          1532          1533          1534          1535 
## -1.0105202187 -0.3840683558 -0.5146145807 -0.5571489860 -1.2891057310 
##          1536          1537          1538          1539          1540 
## -1.0208788696 -0.9937617670 -0.3614346563 -0.6935975512 -0.4962155838 
##          1541          1542          1543          1544          1545 
## -0.9420434717 -0.5413515236 -0.6473603042 -0.9130607360 -0.9432348392 
##          1546          1547          1548          1549          1550 
## -1.1334865878 -0.5593683693 -1.3529221513 -0.6061335079 -1.0595395406 
##          1551          1552          1553          1554          1555 
## -0.5896785632 -0.7302194777 -1.0118767665 -1.1908260773 -1.1619729293 
##          1556          1557          1558          1559          1560 
## -1.1939977297 -0.9288801354 -1.0051261614 -0.7882427110 -1.2604864490 
##          1561          1562          1563          1564          1565 
## -1.2953900079 -1.2052688594 -0.5567611029 -1.0938290066 -0.8595178070 
##          1566          1567          1568          1569          1570 
## -0.4626244672 -0.9891104405 -1.4495653598  0.9449306816  0.8505087835 
##          1571          1572          1573          1574          1575 
## -1.9800616025 -0.1464712504 -0.2068509916 -0.3636697972 -0.9042997365 
##          1576          1577          1578          1579          1580 
##  0.3242887959 -0.4574045628 -1.9887632100  0.8036165350 -0.2036433798

Stanford University (6085513000) possesses the most negative residual value for asthma, indicating that the measure for asthma prevelance here is an underestimate of the reality. I hypothesize that this is the case because, due to the high migration rates in a university setting, PM 2.5 does not control asthma prevelance as strongly. It can take years for PM 2.5 to have its full effects, and people only go to college, in the most basic scenario, for 4 years at a time.